Calibration Loads#

The HOT/COLD load system provides the absolute flux reference for the heterodyne calibration. This page describes how raw load data is processed into the gain calibration factor $\gamma$, receiver temperature $T_{rec}$, and bad channel mask.

Load Extraction#

Calibration subscans are identified by their sobsmode string:

  • HOT — hot load (ambient temperature blackbody)

  • COLD / COL — cold load (typically 77 K LN₂)

  • SKY — sky measurement

  • ZERO — zero-level check

For each calibration subscan, the count data [C, D] is averaged over the dump axis (NaN-aware, skipping padded values) to produce mean hot/cold counts per channel.

Implementation: cal-core/src/math/dump_mean.rs → nan_mean_axis()

Effective Load Temperature#

The hot load is at ambient temperature, but spillover past the load couples to the ambient environment. The effective load temperature corrects for this:

$$ T_{hot,eff}^{sig} = \frac{T_{RJ}(\nu_{sig}, T_{hot})

  • f_{amb} \cdot T_{RJ}(\nu_{sig}, T_{amb})}{1 - f_{amb}} $$

where $f_{amb} = 1 - f_{eff}$ is the ambient coupling fraction and $f_{eff}$ is the forward efficiency.

The sky coupling coefficient relates ambient to effective temperature:

$$ a_{sig} = \frac{T_{RJ}(\nu_{sig}, T_{amb})}{T_{hot,eff}^{sig}} $$

Implementation: cal-io/src/resolve.rs

Gamma (Gain Calibration Factor)#

The gamma factor converts count differences to temperature differences:

$$ \gamma(\nu) = \frac{C_{hot}(\nu) - C_{cold}(\nu)}{T’_{hot}(\nu)

  • T’_{cold}(\nu)} \cdot (g_s x_s + g_i x_i) $$

This is the sensitivity in counts per Kelvin, including the sideband gain weighting.

Implementation: cal-core/src/math/gamma.rs → gain_calibration_formula()

Receiver Temperature#

The Y-factor method yields the primed receiver temperature:

$$ y = \frac{C_{hot}}{C_{cold}} $$

$$ T’{rec} = \frac{T’{hot} - y \cdot T’_{cold}}{y - 1} $$

Converting to single-sideband:

$$ T_{rec,SSB} = \left(T’{rec} - T’{term}\right) \cdot \frac{g_s x_s + g_i x_i}{g_s x_s} $$

where $T’_{term}$ is the sideband-weighted termination temperature (spillover).

Implementation: cal-core/src/math/temperature.rs → t_rec_formula()

Bad Channel Detection#

A channel is flagged as bad if any of the following conditions hold:

  1. $C_{hot} \leq C_{cold}$ — load signal not detected

  2. $(C_{hot} - C_{cold}) < \text{clip_counts} \cdot \max(\text{smoothed}(C_{hot} - C_{cold}))$ — weak relative signal

  3. $T_{rec,SSB} \leq 0$ — unphysical receiver temperature

  4. $T_{rec,SSB} > \text{clip_tsys} \cdot \frac{h \nu_{typ}}{k_B}$ — unrealistically high

The clip_tsys (default 200 K) and clip_counts (default 0.01) thresholds are configurable.

Implementation: cal-core/src/math/temperature.rs → compute_bad_channels()

Per-Channel Load Temperature Tables#

Some receivers provide per-channel RJ load temperatures via the LOAD_TEMP_ARRAY (pre-computed from load emission models). When available, these replace the scalar $T_{RJ}(T_{hot})$ with per-channel values, improving accuracy near band edges where the load is not perfectly isothermal.

Implementation: cal-core/src/scan/cal_load.rs – CalibrationLoad::new_with_load_temps()

Gain Drift Correction (Gain Interpolation)#

When --gain-interpolate is active, raw counts are corrected for receiver gain and noise-temperature drift between the two bracketing HOT/COLD calibration epochs:

$$ C_{corr}(\nu) = \frac{C(\nu)}{1 + w \cdot \Gamma(\nu)}

  • G_1(\nu) , R_1(\nu) , w , \rho(\nu) $$

where $\Gamma$ is the fractional gain change between epochs, $\rho$ the receiver-temperature drift coefficient, and $w$ the time weight.

Time base. The anchors $t_{start}/t_{end}$ are the MJDs of the bracketing COLD subscans — the same instants legacy kalibrate uses (its gain_monitor_start/end_time are the FITS DATE of those COLD subscans, buffers.cpp:1397-1398). The weight $w = (t_{subscan} - t_{start})/(t_{end} - t_{start})$ is computed once per subscan. Legacy refines $t$ per dump when OBSMODE is OTFT/OTFSWA/OTFSWB; this refinement is deliberately dropped. It is exactly equivalent for OBSMODE-empty data (the entire SOFIA parity corpus) and bounded below ~1 mK otherwise — revisit via issue #24 if OBSMODE-set data enters the pipeline.

Implementation: cal-core/src/gain.rs → compute_gain_coefficients(), apply_gain_correction()

Data Flow#

        graph LR
  CS[CalibrationSnapshot<br/>raw HOT/COLD] -->|extract & average| HC[hot_counts, cold_counts<br/>per channel]
  HC --> G[gamma]
  HC --> TR[T_rec_prime, T_rec_SSB]
  HC --> BC[bad_channels mask]
  G --> CL[CalibrationLoad<br/>all derived quantities]
  TR --> CL
  BC --> CL